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Kolmogorov's Heritage in Mathematics / edited by Eric Charpentier, Annick LESNE, Nikolaï K. Nikolski
版 | 1st ed. 2007. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 2007 |
本文言語 | 英語 |
大きさ | VIII, 318 p. 38 illus : online resource |
著者標目 | Charpentier, Eric editor LESNE, Annick editor Nikolski, Nikolaï K editor SpringerLink (Online service) |
件 名 | LCSH:Mathematical logic LCSH:Probabilities LCSH:Dynamical systems LCSH:Fourier analysis LCSH:Topology FREE:Mathematical Logic and Foundations FREE:Probability Theory FREE:Dynamical Systems FREE:Fourier Analysis FREE:Topology |
一般注記 | The youth of Andrei Nikolaevich and Fourier series -- Kolmogorov’s contribution to intuitionistic logic -- Some aspects of the probabilistic work -- Infinite dimensional Kolmogorov equations -- From Kolmogorov’s theorem on empirical distribution to number theory -- Kolmogorov’s ?-entropy and the problem of statistical estimation -- Kolmogorov and topology -- Geometry and approximation theory in A. N. Kolmogorov’s works -- Kolmogorov and population dynamics -- Resonances and small divisors -- The KAM Theorem -- From Kolmogorov’s Work on entropy of dynamical systems to Non-uniformly hyperbolic dynamics -- From Hilbert’s 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov’s Superposition Theorem -- Kolmogorov Complexity -- Algorithmic Chaos and the Incompressibility Method A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov. Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. His contributions are presented, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the current prospects. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than present detailed proofs, the main ideas are described. A bibliography is provided for those who wish to understand the technical details. One can see that sometimes very simple reasoning (with the right interpretation and tools) can lead in a few lines to very substantial results. The Kolmogorov Legacy in Physics was published by Springer in 2004 (ISBN 978-3-540-20307-0) HTTP:URL=https://doi.org/10.1007/978-3-540-36351-4 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783540363514 |
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EB00232819 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA8.9-10.3 DC23:511.3 |
書誌ID | 4000117031 |
ISBN | 9783540363514 |
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